Chapter 1
Examples and Homework Problems
CSE3214 Computer Network
Protocols and Applications
Example 1 (review question 18)
(1) How long does it take a packet of length 1000 bytes to propagate over a link of distance 2500km, propagation speed 2.5x108 m/s, and transmission rate 2 Mbps?(2) More generally, how long does it take a packet of length L to propagate over a link of distance d, propagation speed s, and
transmission rate R bps?
(3) Dose this delay depend on packet length? (4) Does this delay depend on transmission rate?
Solution to Example 1
(1) How long does it take a packet of length 1000 bytes to propagate over a link of distance 2500km, propagation speed 2.5x108 m/s, and transmission rate 2 Mbps?
Ans: (2500*10^3)/(2.5*10^8)=0.01s = 10ms
(2) More generally, how long does it take a packet of length L to propagate over a link of distance d, propagation speed s, and
transmission rate R bps? Ans: d/s
(3) Dose this delay depend on packet length? No (4) Does this delay depend on transmission rate? No
Example 2 (R19)
Suppose Host A wants to send a large file to Host B. The path from Host A to Host B has three links, of rate R1=500kbps,
R2=2Mbps, and R3=1Mbps.
a. Assuming no other traffic in the network, what is the
throughput for the file transfer?
b. Suppose the file is 4 million bytes. Dividing the file size by
the throughput, roughly how long will it take to transfer the file to Host B?
Solution to Example 2
Suppose Host A wants to send a large file to Host B. The path from Host A to Host B has three links, of rate R1=500kbps, R2=2Mbps, and R3=1Mbps.
a. Assuming no other traffic in the network, what is the
throughput for the file transfer? Ans: 500kpbs.
a. Suppose the file is 4 million bytes. Dividing the file size by the
throughput, roughly how long will it take to transfer the file to Host B?
Ans:
(4*10^6)*8/(500*10^3)= 64 seconds
a. Repeat (a) and (b), but now with R2 reduce to 100kpbs.
Example 3 (R21)
Visit the Queuing and Loss applet at the companion web site. What is the maximum emission rate and the minimum
transmission rate? With those rates, what is the traffic intensity? Run the applet with these rates and determine how long it takes for packet loss to occur. Then repeat the experiment a second time and determine again how long it takes for packet loss to occur. Are the values different?
Solution to Example 3
Visit the Queuing and Loss applet at the companion web site. What is the maximum emission rate and the minimum transmission rate?
With those rates, what is the traffic intensity?
Run the applet with these rates and determine how long it takes for packet loss to occur. Then repeat the experiment a second time and determine again how long it takes for packet loss to occur. Are the values different?
Ans:
The maximum emission rate is 500 packets/sec and the
maximum transmission rate is 350 packets/sec.
The corresponding traffic intensity is 500/350 =1.43 > 1.
Loss will eventually occur for each experiment; but the time
when loss first occurs will be different from one experiment to
the next due to the randomness in the emission process.
Packet Loss under TI=1
When the emission and transmission rate are the same, TI=1, the
Example 4 (Problem 2)
The end-to-end delay of sending a packet consisting L bits
from source to destination over a path consisting N links
each of rate R is (NL/R). Generalize this formula for
Solution to Example 4
The end-to-end delay of sending a packet consisting L bits from
source to destination over a path consisting N links each of rate
R is (NL/R). Generalize this formula for sending P such packets
back-to-back over the N links.
Ans:
At time N*(L/R) the first packet has reached the destination,
the second packet is stored in the last router, the third packet is
stored in the next-to-last router, etc. At time N*(L/R) + L/R,
the second packet has reached the destination, the third packet
is stored in the last router, etc. Continuing with this logic, we
see that at time N*(L/R) + (P-1)*(L/R) = (N+P-1)*(L/R) all
packets have reached the destination.
Homework Problems for Chapter 1
Problem 1 (P3)
Consider an application that transmits data at a steady rate (for example, the sender generates an N-bit unit of data every k time units, where k is small and fixed). Also, when such an application starts, it will continue running for a relatively long period of time. Answer the following questions. Briefly justifying your answer:
a. Would a packet-switched network or a circuit-switched
network be more appropriate for this application? Why?
b. Suppose that a packet-switched network is used and the only
traffic in this network comes from such applications as
described above. Furthermore, assume that the sum of the application data rates is less than the capacities of each and every link. Is some form of congestion control needed? Why?
Problem 2 (P6, c & g)
Consider two hosts, A and B, connected by a single link of rate R bps. Suppose that the two hosts are separated by m meters, and suppose the propagation speed along the link is s meters/sec. Host A is to send a packet of size L bits to Host B.
a. Ignoring processing and queuing delay, obtain an expression for the end-to-end delay.
b. Suppose s=2.5*108 meters/sec, L=120 bits, and R=56kbps. Find the
Problem 3(P7)
We consider sending real-time voice from Host A to Host B over a packet-switched network (VoIP). Host A converts analog voice to a
digital 64kpbs bit stream on the fly. Host A then groups the bits into 56-byte packets. There is one link between Hosts A and B, its transmission rate is 2Mbps and its propagation delay is 10msec. As soon as Host B
receives an entire packet. It converts the packet’s bit to an analog signal. How much time elapses from the time a bit is created (from the original analog signal at Host A) until the bit is decoded (as part of the analog signal at Host B)?
Problem 4 (P31)
In modern packet-switched networks, including the Internet, the source host segments long application-layer message (for example, an image or a music file) into smaller packets and sends the packets into the network. The receiver then reassembles the packets back into the original message. We refer to this process as message segmentation. Consider a message that is 8*106 bits
long that is to be sent from Host A to Host B with two packet-switches in between. Suppose each link is 2Mbps. Ignore propagation, queuing, and processing delays.
a. Consider sending the message from A to B without message segmentation. How long does it
take to move the message from Host A to the first packet switch? Keeping in mind that each switch uses store-and-forward packet switching. What is the total time to move the message from A to B?
b. Now suppose that the message is segmented into 800 packets, with each packet being
10,000 bits long. How long does it take to move the first packet from A to the first switch? When the first packet is being sent from the first switch to the second switch, the second packet is being sent from A to the first switch. At what time will the second packet be fully received at the first switch?
c. How long does it take to move the file from A to B when message segmentation is used?
Compare this result with your answer in part (a) and comment.
d. In addition to reducing delay, what are reasons to use message segmentation? e. Discuss the draw-backs of message segmentation.
